Question

Question 9
If the mean of the following data is 20.2, then find the value of p.

$\begin{array}{cccccc}x& 10& 15& 20& 25& 30\\ f& 6& 8& p& 10& 6\end{array}$

Answer 1

We know that,

Mean of the data $\left(\overline{x}\right)=\frac{{\sum }_{i=1}^5{f}_i{x}_i}{{\sum }_{i=1}^5{f}_i}=20.2$ [given]

$\Rightarrow \frac{f_1{x}_1+f_2{x}_2+f_3{x}_3+f_4{x}_4+f_5{x}_5}{f_1+f_2+f_3+f_4+f_5}=20.2$

$\Rightarrow \frac{\left(6\right)\left(10\right)+\left(8\right)\left(15\right)+\left(p\right)\left(20\right)+\left(10\right)\left(25\right)+\left(6\right)\left(30\right)}{6+8+p+10+6}=20.2$

$\Rightarrow \frac{60+120+20p+250+180}{30+p}=20.2$

$\Rightarrow 20p+610=606+20.2p$

$\Rightarrow 610-606=20.2p-20p$

$\Rightarrow \frac{2p}{10}=4$

$\therefore p=10\times 2=20$

Hence, the value of p is 20.